# All positive Beta exponents in a binomial logistic regression

I'm running a regression in which the predictor is a categorical measure of living arrangement (1=two parent household, 2 = single parent, etc). There are 8 total categories in this variable. I'm using them to predict a binary categorical outcome (1=yes and 2=no).

The results I'm getting all have positive B coefficients and Exp(B) values greater than one. I'm interpreting this to mean that, for example, two parent households are more likely to score a 2 than all other living arrangements. However, if this is the case for ALL categories, wouldn't this be impossible? Not sure how every category can be more likely to have the same outcome than every other category.

I'm new to this type of analysis so it's very possible that I'm interpreting the outcome incorrectly. Any help would be greatly appreciated.

• What program are you using? Some programs treat the coding of your response variable differently. In general, it's typical to manually set yes $=1$ and no $=0$. By the way, there is nothing concerning with having $exp(\hat{\beta}) \gt 1$. – StatsStudent Feb 5 at 4:44
• If you can add the actual output that would be helpful. – Yuval Spiegler Feb 5 at 4:49

As StatStudent mentioned in the comment, there is nothing wrong if all is done correctly with all coefficients being larger than 1, for several reasons:

1. If all are larger than 1, it doesn't mean that they are all significant. If they are all significant, than it has a specific meaning to it (see point no.2)
2. They are not really all larger than 1. That would be impossible - they all have a larger than 1 association compared to the omitted category. So, we can say on a category that it has an odds ratio of 1.4 time larger than the omitted category to whatever your dependent variable is.

The thing alluded here is if all is done correctly. By this I mean that the categorical variable needs to be treated properly to have an omitted category. For example, you can recode each category to a binary 0 and 1 variable (e.g., 2_parent [0 no, 1 yes]). In R, you can turn the categorical variable into a factor and R will automatically exclude the first category (which can be changed if needed).

Categorical independent variables need to be parameterized - there are various methods, the most common are dummy coding and effect coding and searching on those terms will give a lot of information, both here and elsewhere. Any decent statistics program (R, SAS, SPSS etc) will do this for you, provided that you write the code correctly (e.g. in SAS, you need a class statement, in R you need to use factor) but, unfortunately, the defaults aren't entirely uniform across programs.

However, in any coding there will be one level that is the reference category and the results for each level that is shown will be compared to that category. SAS and R (regrettably, in my opinion) do not print anything for the reference level - you have to know it's there.

So, you are not necessarily doing anything wrong, but you need to learn about whatever program you are using.